Let $f:[a,b]\rightarrow \mathbb{R}$ bounded and $\omega(f,r)=\sup\{|f(x)-f(y)| \colon x,y \in [a,b], \ |x-y|<r\}$ (called modulus of continuity of $f$ ...

Why nothing is mentioned about the standard deviation of a Bernoulli trial ? Does it even make sense if I try to visualize it ?

Let S be the solid with flat base, whose base is the region in the xy plane defined by the curves $$y=e^x$$,$$y=−3$$,$$x=0$$ and $$x=1$$, and whose cross-se...

I am doing a question from the textbook "Calculus and Statistics" by Gemigani. If $n = 2m$ and $k= 1,2, \ldots ,m$ Prove that $C(n,k)= C(n,n-k)$ Ok so my ...

Expression $$\frac{a}{b+c}+\frac{b}{a+c}+\frac{c}{a+b}$$ takes an integer value $2$ when $a=t, b=t, c=3t$. Are there any other integer values of variables...

For small values of $\theta$, $\sin\theta = \theta$ this must be done in what units radians or degrees Sin (6°)=6 or sin(6)=6

I did the integration by parts and got this expression, but then I am stuck on how to take it further. I tried substituting u=1-x^2, but then I had to do ...

$$\tan81^\circ-\tan63^\circ-\tan27^\circ+\tan9^\circ$$ At first, I tried to break the tangent into multiple angles… $$\text{FAILED}$$ Then I procee...

i was wondering if someone could check my proof $Q= \{a/b , c,d : a,c ∈ \mathbb Z , b,d ∈ N>0\}$ $a/b =x+y$ $a/b -y=x$ proof by contradiction. Let $x-y...

I understand the inverse of e^{x} is the natural logarithm. However I don't understand how the following expression is true: $e^{-\ln x} = e^{\ln(1/x...